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Efficiency of projected score methods in rectangular array asymptotics

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The paper considers a rectangular array asymptotic embedding for multistratum data sets, in which both the number of strata and the number of within-stratum replications increase, and at the same rate. It is shown that under this embedding the maximum likelihood estimator is consistent but not efficient owing to a non-zero mean in its asymptotic normal distribution. By using a projection operator on the score function, an adjusted maximum likelihood estimator can be obtained that is asymptotically unbiased and has a variance that attains the Cramér–Rao lower bound. The adjusted maximum likelihood estimator can be viewed as an approximation to the conditional maximum likelihood estimator.
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Keywords: Asymptotic theory; Neyman–Scott problem; Nuisance parameters; Projected score; Rectangular array

Document Type: Research Article

Affiliations: 1: Frontier Science and Technology Research Foundation, Chestnut Hill, USA 2: Pennsylvania State University, University Park, USA 3: University of Pennsylvania, Philadelphia, USA

Publication date: 2003-02-01

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